ASTR 102 ON-LINE LABORATORY EXERCISE

Spectral Classification & the H-R Diagram

INTRODUCTION
   One of the content objectives for General Education physical science courses at SJSU is to understand "systems of classification". This exercise will examine the classification systems used by astronomers to categorize stellar brightnesses and spectral appearances and will show how patterns revealed by these classifications provide keys to understanding the physical properties of the examined systems.
   Two thousand years ago, Greek astronomers introduced a numerical system to indicate the brightnesses of stars and by the late 19th century that system had been quantitatively formalized into the MAGNITUDE system in which larger numerical values represent fainter stars. Also toward the end of the 19th century astronomers began grouping stars by the visual appearance of their spectra (into SPECTRAL CLASSES). Around 1913 Hertzsprung and Russell independently produced graphs of stellar brightness vs. spectral class (now known as an H-R DIAGRAM). The non-random arrangement of stars in this diagram indicated that most stars (the ones along the Main Sequence) were fundamentally very similar to each other and study of the stellar patterns has proven to be of use in stellar evolution studies, distance determinations and identification of unusual stars. Clusters of stars are of particular usefulness in H-R diagram studies since all the stars in one cluster are at nearly the same distance and formed from the same material at roughly the same time.
   Current theory predicts that massive stars mature more rapidly than smaller ones. In a cluster, stars of all masses are formed and move "quickly" to their appropriate locations along the Main Sequence (larger mass stars are brighter and hotter). They stay there while they fuse H into He in their cores, then evolve through the giant, variable and finally white dwarf regions. More massive stars exhaust their H faster so they are the first to move away from the Main Sequence into these other regions. In fact, the termination point for the Main Sequence determines the age of a star cluster.

PROCEDURE
   In this exercise you will determine the brightnesses (magnitudes) and spectral classes for some stars in a cluster and then use that information to produce an H-R Diagram for the cluster. You will then use that diagram to determine the age and distance of the cluster.

a) MAGNITUDES
   When you pass the mouse over each star in the STAR FIELD picture, the star will be identified by number (there are 15 stars in all). At the right of the STAR FIELD picture is a panel showing magnitude standards, i.e., how bright stars of various brightnesses (magnitudes) appear. Compare each star to the standards and determine the approximate magnitude of each star. The magnitudes of most of the stars will not be exactly that of one of the standards, i.e., you'll need to find standards that bracket the chosen star and then estimate a value between the values given for the standards. Enter the magnitude values in the DATA TABLE.

b) SPECTRAL CLASSES
   If you click the mouse when the cursor is on a star, the spectrum of that star will be displayed. Click on SPECTRAL CLASS SAMPLES to see samples of various spectral classes. The dark lines seen in the spectra are due to absorptions by atoms in the stellar atmospheres and the principal absorbers and their patterns are shown at the top and bottom of the spectral class panel. The spectral classes are idenitified by letters of the alphabet, the modern sequence being O, B, A, F, G, K and M. The spectra gradually alter in appearance, i.e., the prominence of various spectral lines changes, as you move from one of end of the spectral class sequence to the other. The slight variations within a spectral class are specified by 10 subclasses ranging from 0 to 9. For example, the variations between the A0 and F0 classes are denoted as A0, A1, A2, ..., A9, F0. Compare each star to the spectra standards and determine the approximate spectral class and subclass of each star. The spectral classes of most of the stars will not be exactly that of one of the standards, i.e., you'll need to find standards that bracket the chosen star and then estimate a subclass between the values given for the standards. Enter the spectral class determinations in the DATA TABLE.


DATA TABLE
STAR FIELD

Star #
m
Spectral
Class



"Your browser understands the <APPLET> tag but isn't running the applet for some reason.
Do your security settings disallow Java or Active X components?"



c) PLOTTING the H-R DIAGRAM
   When you have completed the Data Table, scroll down to the H-R Diagram. The circled numbers to the right of the graph represent the stars in the Data Table. Using the mouse, "left click" on each number and "drag" it to its appropriate place on the graph, i.e., to the magnitude and spectral class location specified in the Data Table. When completed, this should produce a Main Sequence (a diagonal line of stars trending downward to the right) along with several "non-Main Sequence" stars. Use this diagram as the basis for answering the Questions.


 DATA TABLE
H-R DIAGRAM

Star #
m
Spectral
Class



"Your browser understands the <APPLET> tag but isn't running the applet for some reason.
Do your security settings disallow Java or Active X components?"




QUESTIONS
  1. Enter the Cluster "Name" as displayed at the top left of the "Star Field" image (the name starts with the letters "LT").

            CLUSTER NAME =


  2. In a cluster, stars that are at the top end of the Main Sequence are the ones that are just reaching the point of exhausting their core Hydrogen. Their lifetime is determined by their fuel supply, i.e., their mass, and their fuel usage rate, i.e., their luminosity. You can estimate the Main Sequence lifetime from:  
    LIFETIME  =    Fuel Supply      =      Mass of Star        =  1.00 x 1010  M   years
    Fuel Usage RateLuminosity of StarL

    where M and L are measured in terms of the "solar" mass and luminosity.
    1. From the H-R Diagram you plotted above, estimate the spectral class of the star at the topmost end of the Main Sequence. Enter that spectral class in the box below.

         Spectral Class at MS Turnoff =

    2. Using the graph of Mass vs. Spectral Class for Main Sequence stars, estimate the mass for the spectral class chosen in answer a) and enter that mass in the box below.

          Mass of Star at MS Turnoff = Solar masses

    3. Using the graph of Luminosity vs. Spectral Class for Main Sequence stars, estimate the luminosity for the spectral class chosen in answer a) and enter that luminosity in the box below.
          Luminosity of Star at MS Turnoff = Solar luminosities

    4. Using the "lifetime" formula above, calculate the Main Sequence lifetime of the star at the Main Sequence turnoff point. This is the age of the entire star cluster. Place this value in the box below.
         Age of Star Cluster = years

    5. How many "significant figures" did you keep in your age calculation? Why did you keep that number of significant figures?



  3. The distance to a star can be calculated by comparing its apparent magnitude m (how bright it appears to be) to its absolute magnitude M (how bright it really is). The formula for making this calculation is:
    M = m + 5 - 5 Log10(Distance)      or      DISTANCE (in parsecs) = 10 (m - M + 5) / 5
     For a cluster, this calculation is best done with Main Sequence stars since their magnitudes are well-known (compared to the non-Main Sequence stars which are much more scattered in brightness). To minimize experimental uncertainty, you'll compare the m and M values for several of the Main Sequence stars in your cluster and then form an average m - M to use in calculating the distance.
    1. For three different stars along the Main Sequence in your cluster, enter their apparent magnitudes (m) in the table below. From the graph of Absolute Magnitude vs. Spectral Class for Main Sequence stars, estiamte the absolute magnitudes (M) for those stars and enter the values in the table below. Finally, subtract M from m and enter those values in the table below.

      Star #mMm - M

    2. Take the average of the three m - M values in the table above and enter that value in the box below.

         Average m - M value =

    3. Use the average m - M value in the DISTANCE formula (you'll need a calculator that can do the function '10x ') to find the distance to the cluster in "parsecs". Enter that value in the box below.

         Distance to cluster = parsecs

    4. A "parsec" is equal to 3.26 light-years. Use this factor to convert the distance from parsecs to light-years. Enter that value in the box below.

         Distance to cluster = light-years

    5. How many "significant figures" did you keep in your distance determination? Why did you keep that number of significant figures?



  4. Of the stars shown in this cluster, which one (identify it by its number) was originally the most massive? Explain clearly.



  5. Describe in words how the spectrum of an F2 star differs from that of an F7 star, i.e., specify which line patterns are more prominent in one class relative to the other.


  6. Because there are only 15 stars in this cluster and because spectral class estimates are a bit imperfect, the Main Sequence termination point for your cluster has some uncertainty. For example, you might estimate that it terminates at A5 but anything from A3 to A7 would probably be equally justified by your data. Since the age of the cluster depends on the mass of the stars at the termination point, any uncertainty in the spectral class will lead to an uncertainty in the age. Suppose you had two clusters, one with an estimated termination point at B5 and the other at F5. Looking at the graph of Mass vs. Spectral Class, in which case (the B5 termination or the F5 termination) will the estimated mass (and age) have the greater percentage error if the termination point is uncertain by 2 or 3 subclasses? Explain clearly.



SUBMITTING the REPORT

   This exercise uses applets (for the STAR FIELD and H-R DIAGRAM) and there are "security issues" with such things. As a result, it is not an easy thing to get this report back to me. You have three possibilities:

  1. Print out the data table and H-R Diagram and the answers to the questions, staple them together, put your name on it and bring it to my office (SCI 264) or put it in my mailbox in the department office (SCI 148).

  2. Print out the data table and H-R Diagram and the answers to the questions and "snail mail" the printouts to me at:

      Dr. Les Tomley
      Department of Physics
      San Jose State University
      San Jose, CA 95192-1600

  3. Use the following procedure to create "images" of the relevant report segments and then email the images to me as attachments. Here's how you'd do that with a PC (I assume Mac users have a similar procedure, but you're on your own there).

    1. Center the part of the page you want to copy in the browser screen, i.e., make sure all the parts of the table, graph or questions show on the screen.
    2. Hold down the "ALT" button and simultaneously press the "Print Screen" key, i.e., hit "Alt-Print Screen". This puts a copy of the screen on the "clipboard".
    3. Minimize or move the browser window so you can open your "Paint" program (under Programs/Accessories from the Start menu).
    4. From the "Edit" menu in "Paint", choose "Paste". This will copy the image on the clipboard into Paint.
    5. From the "File" menu in "Paint", choose "Save As ..." and name and save the image someplace on your computer, e.g., the Desktop. I recommend you use the "JPEG" format rather than the "BMP" format.
    6. Maximize the browser and repeat steps a) through e) for each part of the exercise you want to send to me. I'll want the data table and H-R Diagram graph and the answers to the questions in the report.
    7. When you have the images of all the things you want, send me an e-mail (LesTomley@sjsu.edu) and attach the image files. You can use the body of the e-mail to add any additional information, if necessary.
[ Back ]    [ Astro Philes Home Page ]     [ SJSU Home Page ]
©2007 Leslie J. Tomley